Diagram automorphisms and Rank-Level duality

TL;DR

This paper investigates how diagram automorphisms influence rank-level duality, establishing new symplectic dualities on genus zero curves and connecting them to existing representation-theoretic dualities.

Contribution

It introduces new symplectic rank-level dualities on genus zero curves and links them to known representation-theoretic dualities via diagram automorphisms.

Findings

New symplectic rank-level dualities on genus zero curves.

Connection between rank-level dualities and parabolic strange duality.

Proof that certain dualities can be derived from diagram automorphisms.

Abstract

We study the effect of diagram automorphisms on rank-level duality. We use it to prove new symplectic rank-level dualities on genus zero smooth curves with marked points and chosen coordinates. We also show that rank-level dualities for the pair sl(r), sl(s) in genus 0 arising from representation theory can also be obtained from the parabolic strange duality proved by R. Oudompheng.